Download Elementary Statistics and Inference Elementary Statistics and

Elementary Statistics and
Inference
22S:025 or 7P:025
Lecture 8
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Elementary Statistics and
Inference
22S:025 or 7P:025
Chapter 6
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7.) Measurement Error
A.
Introduction
The difference between a measurement (score)
and the “true” value of the measurement is called
“chance” error –
X=T–E
Score = True Value – Error
The less the values of E, the more reliable the
measurement.
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7.) Measurement Error (cont.)
B.
Chance Error
„
Precision of measurements at the National Bureau of
Standards.
„
International Prototype Kilogram (kilogram) is the
“standard weight” of one kilogram. All other weights
are defined and compared to the kilogram under
standard conditions – Paris.
1 pound = .4539237 of one kilogram
2.203 pounds = 1 kilogram
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7.) Measurement Error (cont.)
„
The USA was assigned kilogram #20 (k20).
„
The US National Bureau of Standards (1940) has a
NBIO – the weight of 10 grams, which is the weight of
about 2 nickels. The NB weighs
g NBIO about every
y week
to determine the reliability of the measurement process.
On page 99 of the text – a display of 100 measurements
of NBIO, and the measurements represent micrograms
below 10 grams. Note the variability of the
measurements. – This is due to chance error.
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7.) Measurement Error (cont.)
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7.) Measurement Error (cont.)
„
The average of the 100 measurements is 405
micrograms below 10 grams and the standard deviation
was 6 micrograms (chance error).
„
The NB does these repeated measurements from time to
time to check the consistency of the instruments used to
weigh NBIO.
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7.) Measurement Error (cont.)
„
The SD of a series of measurements is the likely size of the
“chance error” of the measurements.
X = T + E (see p. 101)
individual measurement or score = exact value or
true value + chance error
„
Such measurement error occurs with nearly all behavioral
research because the measurement process is not perfect –
e.g., heights, weights, abilities, attitudes, physiological traits.
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7.) Measurement Error (cont.)
C.
Outliers
If the measurements are normally distributed, you
would expect 95% of them to be within 2 standard
deviations of the mean.
mean Any measurement that is more
than 3 standard deviations from the mean is
considered highly unusual (outlier).
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7.) Measurement Error (cont.)
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7.) Measurement Error (cont.)
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7.) Measurement Error (cont.)
D.
Bias
If some aspect of the measurement process is affected
systematically – the measuring process is biased (i.e.,
not truly representative of the true measurement
process). E.g., if heights of men were determined by
only measuring the heights of college basketball
players,
l
th
the measurements
t would
ld b
be bi
biased.
d
Or, if the measurement of heights of men was done
with a “cloth tape” that could stretch or shrink,
depending on humidity, the measurements would be
biased.
X=T+E+B
measurement = exact value + chance error + bias
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7.) Measurement Error (cont.)
E.
Review Exercises – (pages 104-105) #4, 5
F.
Special Review Exercises – (pages 105-108) #2, 3, 4,
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6,
9, 11
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7.) Measurement Error (cont.)
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7.) Measurement Error (cont.)
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7.) Measurement Error (cont.)
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7.) Measurement Error (cont.)
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7.) Measurement Error (cont.)
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